Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 24 May 2014
Posts: 13
Location: Brazil

Machine M and Machine N working alone at their constant rate
[#permalink]
Show Tags
26 Jul 2014, 10:07
Question Stats:
47% (02:23) correct 53% (02:08) wrong based on 568 sessions
HideShow timer Statistics
Machine M and Machine N working alone at their constant rates, non stop, produced 6000 and 8000 nails respectively. Did machine M work longer than machine N? (1) Machine N produces 2000 more nails than machine M in one hour when each machine work at its constant rate (2) Machine N produces twice as much as machine M in one hour when each machine work at its constant rate
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: Machine M and Machine N working alone at their constant rate
[#permalink]
Show Tags
26 Jul 2014, 10:37
Machine M and Machine N working alone at their constant rates, non stop, produced 6000 and 8000 nails respectively. Did machine M work longer than machine N?(1) Machine N produces 2000 more nails than machine M in one hour when each machine work at its constant rate. If the rate of M is 2,000 nails per hour and the rate of N is 4,000 nails per hour, then to produce 6,000 nails, M needs 3 hours and to produce 8,000 nails N, needs 2 hours. In this case M worked longer than N. If the rate of M is 6,000 nails per hour and the rate of N is 8,000 nails per hour, then to produce 6,000 nails, M needs 1 hours and to produce 8,000 nails N, needs 1 hour. In this case M did not work longer than N. Not sufficient. (2) Machine N produces twice as much as machine M in one hour when each machine work at its constant rate. In the time M needs to produce 6,000 nails, N can produce 12,000 nails, thus it can produce 8,000 nails in less time than M can produce 6,000 nails. Sufficient. Answer: B.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Director
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 796
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)

Re: Machine M and Machine N working alone at their constant rate
[#permalink]
Show Tags
05 Sep 2014, 07:22
Machine M and Machine N working alone at their constant rates, non stop, produced 6000 and 8000 nails respectively. Did machine M work longer than machine N? Let N is number of nails machine N produced. Let M is number of nails machine M produced. And x and y are respective time each machine took to produce 6000 and 8000 nails. (1) Machine N produces 2000 more nails than machine M in one hour when each machine work at its constant rate Given N= M + 2000 Mx = 6000 (1) Ny = 8000 ==> (M+2000)y=8000 (2) Solve 1 and 2 to find ratio of x/y. \((\frac{6000}{x}+2000)y=8000\) We can not reduce this equation in \(x/y\) form. Thus, (1) insufficient. (2) Machine N produces twice as much as machine M in one hour when each machine work at its constant rate. N=2M Mx = 6000 (1) Ny = 8000 ==> 2My=8000 (2) \(2y\frac{6000}{x}=8000\) Solve for \(x/y\); we can calculate x:y. Thus, statement (2) is sufficient.
_________________
Piyush K
 Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison Don't forget to press> Kudos My Articles: 1. WOULD: when to use?  2. All GMATPrep RCs (New) Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".



Intern
Joined: 15 Sep 2013
Posts: 1

Re: Machine M and Machine N working alone at their constant rate
[#permalink]
Show Tags
07 Sep 2014, 09:33
Hi Bunuel,
Why are we rounding off the number of hours here? Am i missing something in the question, why arent we considering minutes, for which im getting the first statement as being sufficient. Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: Machine M and Machine N working alone at their constant rate
[#permalink]
Show Tags
07 Sep 2014, 09:43



Current Student
Joined: 06 Mar 2014
Posts: 247
Location: India
GMAT Date: 04302015

Re: Machine M and Machine N working alone at their constant rate
[#permalink]
Show Tags
07 Sep 2015, 04:15
Bunuel wrote: Machine M and Machine N working alone at their constant rates, non stop, produced 6000 and 8000 nails respectively. Did machine M work longer than machine N?
(1) Machine N produces 2000 more nails than machine M in one hour when each machine work at its constant rate.
If the rate of M is 2,000 nails per hour and the rate of N is 4,000 nails per hour, then to produce 6,000 nails, M needs 3 hours and to produce 8,000 nails N, needs 2 hours. In this case M worked longer than N.
If the rate of M is 6,000 nails per hour and the rate of N is 8,000 nails per hour, then to produce 6,000 nails, M needs 1 hours and to produce 8,000 nails N, needs 1 hour. In this case M did not work longer than N.
Not sufficient.
(2) Machine N produces twice as much as machine M in one hour when each machine work at its constant rate. In the time M needs to produce 6,000 nails, N can produce 12,000 nails, thus it can produce 8,000 nails in less time than M can produce 6,000 nails. Sufficient.
Answer: B. The highlighted part: If the question is to produce 6000 nails then definitely M needs 1 hour but N with a rate of 8000 nails per hour would need less than an hour right? Please clarify if possible. Thank you.



Math Expert
Joined: 02 Sep 2009
Posts: 50007

Re: Machine M and Machine N working alone at their constant rate
[#permalink]
Show Tags
07 Sep 2015, 05:06
earnit wrote: Bunuel wrote: Machine M and Machine N working alone at their constant rates, non stop, produced 6000 and 8000 nails respectively. Did machine M work longer than machine N?
(1) Machine N produces 2000 more nails than machine M in one hour when each machine work at its constant rate.
If the rate of M is 2,000 nails per hour and the rate of N is 4,000 nails per hour, then to produce 6,000 nails, M needs 3 hours and to produce 8,000 nails N, needs 2 hours. In this case M worked longer than N.
If the rate of M is 6,000 nails per hour and the rate of N is 8,000 nails per hour, then to produce 6,000 nails, M needs 1 hours and to produce 8,000 nails N, needs 1 hour. In this case M did not work longer than N.
Not sufficient.
(2) Machine N produces twice as much as machine M in one hour when each machine work at its constant rate. In the time M needs to produce 6,000 nails, N can produce 12,000 nails, thus it can produce 8,000 nails in less time than M can produce 6,000 nails. Sufficient.
Answer: B. The highlighted part: If the question is to produce 6000 nails then definitely M needs 1 hour but N with a rate of 8000 nails per hour would need less than an hour right? Please clarify if possible. Thank you. How does N, at the rate of 8,000 nails per hour, need more than an hour to produce 8000 nails? It will need exactly 1 hour. Again, the question asks: did machine M (which produced 6000 nails) work longer than machine N (which produced 8000 nails)? If the rate of M is 6,000 nails per hour and the rate of N is 8,000 nails per hour, then to produce 6,000 nails, M needs 1 hours and to produce 8,000 nails N, needs 1 hour. In this case M did not work longer than N.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Current Student
Joined: 06 Mar 2014
Posts: 247
Location: India
GMAT Date: 04302015

Re: Machine M and Machine N working alone at their constant rate
[#permalink]
Show Tags
07 Sep 2015, 08:06
Bunuel wrote: earnit wrote: Bunuel wrote: Machine M and Machine N working alone at their constant rates, non stop, produced 6000 and 8000 nails respectively. Did machine M work longer than machine N?
(1) Machine N produces 2000 more nails than machine M in one hour when each machine work at its constant rate.
If the rate of M is 2,000 nails per hour and the rate of N is 4,000 nails per hour, then to produce 6,000 nails, M needs 3 hours and to produce 8,000 nails N, needs 2 hours. In this case M worked longer than N.
If the rate of M is 6,000 nails per hour and the rate of N is 8,000 nails per hour, then to produce 6,000 nails, M needs 1 hours and to produce 8,000 nails N, needs 1 hour. In this case M did not work longer than N.
Not sufficient.
(2) Machine N produces twice as much as machine M in one hour when each machine work at its constant rate. In the time M needs to produce 6,000 nails, N can produce 12,000 nails, thus it can produce 8,000 nails in less time than M can produce 6,000 nails. Sufficient.
Answer: B. The highlighted part: If the question is to produce 6000 nails then definitely M needs 1 hour but N with a rate of 8000 nails per hour would need less than an hour right? Please clarify if possible. Thank you. How does N, at the rate of 8,000 nails per hour, need more than an hour to produce 8000 nails? It will need exactly 1 hour. Again, the question asks: did machine M (which produced 6000 nails) work longer than machine N ( which produced 8000 nails)? If the rate of M is 6,000 nails per hour and the rate of N is 8,000 nails per hour, then to produce 6,000 nails, M needs 1 hours and to produce 8,000 nails N, needs 1 hour. In this case M did not work longer than N. Got it. Its not the common number that the machines are expected to produce. That part slipped out when exploring the options. Key take away: if there is a common number required to produce then even (1) would be sufficient. But not in the above case.



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6390
GPA: 3.82

Machine M and Machine N working alone at their constant rate
[#permalink]
Show Tags
08 Sep 2015, 07:38
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution. Machine M and Machine N working alone at their constant rates, non stop, produced 6000 and 8000 nails respectively. Did machine M work longer than machine N? (1) Machine N produces 2000 more nails than machine M in one hour when each machine work at its constant rate (2) Machine N produces twice as much as machine M in one hour when each machine work at its constant rate In the original condition, r1*t1=6000, r2*t2=8000 and throw some transformation we have t1=6000/r1, t2=8000/r2 and 6000/r1>8000/r2, 3r2>4r1?, therefore the question is all about comparing r1 and r2. We have 4 variables (r1,r2,t1,t2), 2 equations (r1*t1=6000, r2*t2=8000) therefore we need 2 more equations and therefore C is likely the answer. Using both 1) & 2) together, r2=r1+2000, r2=2r1 gives us r1=2000, r2=4000 and thus C is the answer. But such trivial conditions are rarely the answer, so we might try it separately again. Using 1), 2)separately, (from Common mistake type 4(A), in case of 2) substituting r2=2r1 to 3r2>4r1? gives us 3*2r1>4r1?, 6>4. Therefore the answer is yes, and the condition is sufficient. Therefore the answer is B. (when looking at conditions 1), 2) if one is given by value and the other is given by ratio, the one with ratio is usually the answer. That's why we just calculated using con 1) here. )
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Intern
Joined: 30 Aug 2016
Posts: 5
Location: Italy
GPA: 3.83

Re: Machine M and Machine N working alone at their constant rate
[#permalink]
Show Tags
31 Dec 2016, 03:52
Here is my approach
Is 6000/(rate of m = rm) > 8000 / (rate of n = rn) ? <> Is 6/rm > 8/rn? <> Is 6 rn > 8 rm ?
St. 1: rn = rm + 2000 > Is 6 rm + 12000 > 8 rm ? Here we get a condition, i.e. rm < 6000 that is not verified a priori > NOT SUFF
St. 2: rn = 2 rm > Is 12 rm > 8 rm ? Yes because rm >0 > SUFF
B



NonHuman User
Joined: 09 Sep 2013
Posts: 8473

Re: Machine M and Machine N working alone at their constant rate
[#permalink]
Show Tags
25 Jan 2018, 17:41
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: Machine M and Machine N working alone at their constant rate &nbs
[#permalink]
25 Jan 2018, 17:41






